Gravitational effects upon cosmological phase transitions

The effects of spacetime curvature upon phase transitions in an expanding universe are investigated. We consider a Robertson-Walker model which is a radiation-dominated universe at early times and becomes de Sitter space at later times. In this universe the stability of a field theory containing a pair of interacting scalar fields is studied in first-order perturbation theory. It is noted that the crucial quantity in the stability analysis is 〈^2〉, where is a free scalar field. The behavior of 〈^2〉 as a function of time is investigated, where both thermal and vacuum contributions are taken into account. It is shown that this behavior can be strongly affected by the coupling to the background gravitational field. Such coupling can cause 〈^2〉 to decrease more slowly or even grow as the universe expands. This behavior can alter the evolution of the system and can result in either stabilization of an otherwise unstable field configuration or destabilization of an otherwise stable configuration.